By law, if there is a child under the age of 6 your landlord is responsible for making sure there is no lead exposure risk. The landlord should have given you lead paint disclosure form and information. If it is a new landlord they may just be ignorant and presumably will be cooperative once they are informed about the laws in massachusetts regarding lead paint. You should realize it will cost your landlord 10s of thousands of dollars to de-lead, so reluctance is somewhat understandable but definitely illegal. You will not have to pay, but your landlord will pay dearly.
Your little one is surely fine at this point - and a simple blood test (finger stick, not even a blood draw is necessary) can put your mind at ease. Ask your pediatrician.
Best of luck.